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Square Root of 193

The square root of 193 is expressed as √193 in the radical form and as (193)^½ or (193)^0.5 in the exponent form. The square root of 193 rounded up to 8 decimal places is 13.89244399. It is the positive solution of the equation x² = 193.

Square Root of 193: 13.892443989449804
Square Root of 193 in exponential form: (193)^½ or (193)^0.5
Square Root of 193 in radical form: √193

Square Root of 193

1.	What is the Square Root of 193?
2.	How to find the Square Root of 193?
3.	Is the Square Root of 193 Irrational?
4.	FAQs

What is the Square Root of 193?

The square root of 193, (or root 193), is the number which when multiplied by itself gives the product as 193. Therefore, the square root of 193 = √193 = 13.892443989449804.

☛ Check: Square Root Calculator

How to Find Square Root of 193?

Square Root of 193 by Long Division Method

Value of √193 by Long Division Method

Explanation:

Forming pairs: 01 and 93
Find a number Y (1) such that whose square is <= 1. Now divide 01 by 1 with quotient as 1.
Bring down the next pair 93, to the right of the remainder 0. The new dividend is now 93.
Add the last digit of the quotient (1) to the divisor (1) i.e. 1 + 1 = 2. To the right of 2, find a digit Z (which is 3) such that 2Z × Z <= 93. After finding Z, together 2 and Z (3) form a new divisor 23 for the new dividend 93.
Divide 93 by 23 with the quotient as 3, giving the remainder = 93 - 23 × 3 = 93 - 69 = 24.
Now, let's find the decimal places after the quotient 13.
Bring down 00 to the right of this remainder 24. The new dividend is now 2400.
Add the last digit of quotient to divisor i.e. 3 + 23 = 26. To the right of 26, find a digit Z (which is 8) such that 26Z × Z <= 2400. Together they form a new divisor (268) for the new dividend (2400).
Divide 2400 by 268 with the quotient as 8, giving the remainder = 2400 - 268 × 8 = 2400 - 2144 = 256.
Bring down 00 again. Repeat above steps for finding more decimal places for the square root of 193.

Therefore, the square root of 193 by long division method is 13.8 approximately.

Is Square Root of 193 Irrational?

The actual value of √193 is undetermined. The value of √193 up to 25 decimal places is 13.89244398944980450843255. Hence, the square root of 193 is an irrational number.

☛ Also Check:

Square Root of 29 - √29 = 5.38516
Square Root of 54 - √54 = 7.34847
Square Root of 169 - √169 = 13
Square Root of 625 - √625 = 25
Square Root of 96 - √96 = 9.79796
Square Root of 116 - √116 = 10.77033
Square Root of 90 - √90 = 9.48683

Square Root of 193 Solved Examples

Example 1: Solve the equation x² − 193 = 0

Solution:

x² - 193 = 0 i.e. x² = 193
x = ±√193
Since the value of the square root of 193 is 13.892,
⇒ x = +√193 or -√193 = 13.892 or -13.892.
Example 2: If the area of a circle is 193π in². Find the radius of the circle.

Solution:

Let 'r' be the radius of the circle.
⇒ Area of the circle = πr² = 193π in²
⇒ r = ±√193 in
Since radius can't be negative,
⇒ r = √193
The square root of 193 is 13.892.
⇒ r = 13.892 in
Example 3: If the surface area of a cube is 1158 in². Find the length of the side of the cube.

Solution:

Let 'a' be the length of the side of the cube.
⇒ Area of the cube = 6a² = 1158 in²
⇒ a = ±√193 in
Since length can't be negative,
⇒ a = √193
We know that the square root of 193 is 13.892.
⇒ a = 13.892 in

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FAQs on the Square Root of 193

What is the Value of the Square Root of 193?

The square root of 193 is 13.89244.

Why is the Square Root of 193 an Irrational Number?

The number 193 is prime. This implies that the number 193 is pairless and is not in the power of 2. Therefore, the square root of 193 is irrational.

What is the Square of the Square Root of 193?

The square of the square root of 193 is the number 193 itself i.e. (√193)² = (193)^2/2 = 193.

What is the Value of 18 square root 193?

The square root of 193 is 13.892. Therefore, 18 √193 = 18 × 13.892 = 250.064.

What is the Square Root of -193?

The square root of -193 is an imaginary number. It can be written as √-193 = √-1 × √193 = i √193 = 13.892i
where i = √-1 and it is called the imaginary unit.

Evaluate 9 plus 2 square root 193

The given expression is 9 + 2 √193. We know that the square root of 193 is 13.892. Therefore, 9 + 2 √193 = 9 + 2 × 13.892 = 9 + 27.785 = 36.785

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